That is not a requirement in most codes.  It may be a requirement on a WPS, company requirements,  or even in project specifications. It is an extensively talked about subject and may have quite a few opinions.

Often times the number of 2-1/2 times the core diameter comes up. It is a "wives tale" level requirement if its taught as something a code said and does not tell you which code! That number can be found in some the AWS A5.x filler metal specifications but is only for certain tests to qualify the filler metals.

If you "know" that it must not be more than 3X, then you gained that knowledge somewhere. Take a look at that "source" and see if any references are made.

If you want to do some research on many of the fine opinions used in this forum, check out the search results in the following link or use the search menu at the top of the page.

https://app.aws.org/forum/forum_search.pl?words=width&user=&board=0&field=subject&min=&max=&order=desc.